Robust Lagrangian Surface Propagation with Topological Control

DMS-0310446John C.作者声明：哈特Heath，Xiangmin Jiao，and John M. Sullivan这个合作项目在DMS-0310642和DMS-0310354下资助，是一个CARGO全团队奖，在征求http://www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm.Level下做出。集合隐含地表示一个移动的界面表面，它自然地适应奇点和拓扑变化，但代价是浪费的体积欧拉表示，它不提供对水平集拓扑的控制。 我们的项目将开发新的方法来跟踪接口使用更有效的拉格朗日surfacemesh。 通过对不稳定性和拓扑变化的仔细预测，我们将解决困扰以前拉格朗日方法的界面传播的数值、几何和拓扑困难。结果将是界面表面运动的更快和更紧凑的模拟，以及检测和控制其拓扑变化的能力。移动边界或界面表面是各种物理现象的组成部分，例如固化、挤出、多相流动和流体-固体相互作用。 这种现象的数值模拟需要可靠和有效的方法来传播和跟踪这样的移动表面。 我们项目的重点是开发新的方法，提供更好的控制表面传播，同时也获得更高的计算效率比现有的方法。一个具体的应用，我们将考虑在固体推进剂火箭发动机的燃烧模拟，这是UIUC的先进火箭模拟中心（CSAR）的主要重点。 这项工作将导致火箭发动机设计的更有效和更准确的虚拟原型，从而导致更安全和更有效的固体火箭助推器，例如为美国航天飞机提供动力的助推器。

DMS-0310446John C. Hart, Michael T. Heath, Xiangmin Jiao, and John M. SullivanThis collaborative project funded under DMS-0310642 and DMS-0310354 is a CARGO full team award made under solicitation http://www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm.Level sets represent a moving interface surface implicitly, whichnaturally accommodates singularities and topology changes, but at theexpense of a wasteful volumetric Eulerian representation that provides nocontrol over the topology of the level set. Our project will develop newmethods for tracking interfaces using a more efficient Lagrangian surfacemesh. Through careful prediction of instabilities and topology changes,we will address the numerical, geometric, and topological difficultiesthat have plagued previous Lagrangian approaches to interface propagation.The result will be faster and more compact simulations of the motion ofinterface surfaces, as well as the ability to detect and control changesin their topology.Moving boundary or interface surfaces are an integral part of a widevariety of physical phenomena, such as solidification, extrusion,multiphase flow, and fluid-solid interaction. Numerical simulations ofsuch phenomena require reliable and efficient methods for propagating andtracking such moving surfaces. The focus of our project is to developnew methods that provide greater control over surface propagation whilealso attaining greater computational efficiency than existing methods.One specific application we will consider is the simulation of combustionin solid propellant rocket motors, which is the primary focus of UIUC'sCenter for Simulation of Advanced Rockets (CSAR). This work will resultin more efficient and more accurate virtual prototyping of rocket motordesigns, leading to safer and more efficient solid rocket boosters,such as those powering the U.S. Space Shuttle.